Raheem Sterling celebrates after scoring the second goal for Liverpool. (Reuters)

A goal in each half from Philippe Coutinho and Raheem Sterling gave Liverpool a hard fought 2-0 win over Southampton at St. Mary’s in the Premier League on Sunday.

The result moves Liverpool into sixth and only two points behind Manchester United, who still occupy fourth in the table despite losing 2-1 to Swansea on Saturday.

For Southampton, defeat dents its own hopes of qualifying for next season’s Champions League. The team is now only a point above Liverpool in fifth.

”It was an outstanding win for us,” Liverpool manager Brendan Rodgers said. ”To come here on the back of a tough European game (against Besiktas in the Europa League on Thursday) and not concede and score two goals really shows the level the players are working at.”

In blustery wind and heavy rain on the south coast, Coutinho put Liverpool ahead after only three minutes with a sensational strike.

The Brazil international collected a pass 25 yards out from Lazar Markovic, before turning towards Southampton’s goal and curling a powerful strike beyond the reach of goalkeeper Fraser Forster, with the ball crashing in off the underside of the crossbar.

The first five minutes were frenetic and either side of Coutinho’s goal, Southampton had two strong penalty appeals rejected, both involving attacking midfielder Filip Djuricic on his first start for the club since arriving on loan from Benfica.

He went tumbling in the area under pressure from Emre Can and was incredulous when referee Keven Friend waved play on but television replays suggested contact was minimal.

But Djuricic was then felled by Joe Allen as he weaved into the penalty area and this time, replays showed contact was much stronger, yet still nothing was given.

The decisions incensed an already fiery home crowd, who were watching two former players in action for Liverpool having departed Southampton last year.

Adam Lallana, a former captain at St. Mary’s, was booed relentlessly, as was defender Dejan Lovren, who was making a rare start against his former club in place of the injured Mamadou Sakho.

The intensity of the game soon plateaued but Southampton had another contentious decision go against them on the stroke of halftime.

Eljero Elia raced on to a high ball over the top of Liverpool’s defense but as he tried to lift the ball over the onrushing Simon Mignolet, the ball hit the goalkeeper’s arm when he was on the edge of his penalty area.

Elia was convinced Mignolet had handled outside the box but once again, to the outrage of Southampton’s players and fans, referee Friend played on.

Morgan Schneiderlin replaced Steven Davis for Southampton for the start of the second half, while Liverpool also substituted Markovic for Alberto Moreno.

Schneidlerin’s presence in midfield allowed Southampton to enjoy the majority of possession in the second period but Liverpool’s back three of Martin Skrtel, Lovren and Can continued to nullify Southampton’s attacking threat.

Sadio Mane’s introduction in the 56th almost produced an instant equalizer for Southampton, but Skrtel charged down his fierce strike from the left corner of the penalty area.

Liverpool continued to defend stubbornly and eventually hit on the counter to double its lead in the 73rd. Moreno raced down the left and crossed into the area, where defender Matt Targett slipped as he attempted to clear the ball. Sterling pounced on the loose ball, drilling a low effort past Forster to secure Liverpool’s win.

Southampton manager Koeman was frustrated his side did not make its possession of the ball count against Liverpool, but refused to get carried away criticising the referee.

”We had really good movements in attack,” Koeman said. ”Maybe we were a little but unlucky with the decisions in the first half, but they scored a great goal and then it is always difficult.”